Comprehensive Module List¶
Note
This list is currently sorted in alphabetical order w.r.t. the module names.
It can be updated semi-automatically by running in src/sage/combinat
:
find -name "*.py*" | grep -v pycache | sed 's|\.pyx\?$||; s|\./| sage/combinat/|' | LANG=en_US.UTF-8 LC_COLLATE=C sort > /tmp/module_list.rst
and copy pasting the result back there.
Todo
See upstream Issue #17421 for desirable improvements.
- Abstract recursive trees
- Affine permutations
- Algebraic combinatorics
- Combinatorics
- Alternating sign matrices
- Backtracking
- Baxter permutations
- A bijectionist’s toolkit
- Binary recurrence sequences
- Binary trees
- Blob algebras
- Cartesian products
- Partitions, tableaux, and others
- Combinatorial Hopf algebras
- Poirier-Reutenauer Hopf algebra of standard tableaux
- Word quasi-symmetric functions
- Cluster algebras and quivers
- Cluster seeds
- Interactive display of quivers
- mutation_class
- Helper functions for mutation types of quivers
- Quiver
- Quiver mutation types
- Cluster complex (or generalized dual associahedron)
- Colored permutations
- Combinatorial functions
- Fast computation of combinatorial functions (Cython + mpz)
- Combinations
- Combinatorial maps
- Integer compositions
- Signed compositions
- Composition tableaux
- Constellations
- Cores
- Counting
- Affine crystals
- Affine factorization crystal of type \(A\)
- Affinization crystals
- Alcove paths
- Crystals
- Benkart-Kang-Kashiwara crystals for the general-linear Lie superalgebra
- Catalog of crystals
- Catalog of elementary crystals
- Catalog of crystal models For \(B(\infty)\)
- Catalog of crystal models for Kirillov-Reshetikhin crystals
- An introduction to crystals
- Direct sum of crystals
- Elementary crystals
- Fast rank two crystals
- Fully commutative stable Grothendieck crystal
- Crystals of generalized Young walls
- Highest weight crystals
- Induced crystals
- \(\mathcal{B}(\infty)\) crystals of tableaux in nonexceptional types and \(G_2\)
- Crystals of Kac modules of the general-linear Lie superalgebra
- Kirillov-Reshetikhin crystals
- Kyoto path model for affine highest weight crystals
- Crystals of letters
- Littelmann paths
- Crystals of modified Nakajima monomials
- Crystal of Bernstein-Zelevinsky multisegments
- Crystal of Mirković-Vilonen polytopes
- \(\mathcal{B}(\infty)\) crystal of PBW monomials
- PBW data
- Polyhedral realization of \(B(\infty)\)
- Spin crystals
- Star-crystal structure on \(B(\infty)\)
- Subcrystals
- Tensor products of crystals
- Tensor products of crystal elements
- Virtual crystals
- Cyclic sieving phenomenon
- De Bruijn sequences
- Decorated permutations
- Degree sequences
- Derangements
- Descent algebras
- Combinatorial designs and incidence structures
- Balanced incomplete block designs (BIBD)
- Block designs
- Covering arrays
- Covering designs: coverings of \(t\)-element subsets of a \(v\)-set by \(k\)-sets
- Database of small combinatorial designs
- Catalog of designs
- Cython functions for combinatorial designs
- Difference families
- Difference matrices
- Evenly distributed sets in finite fields
- External representations of block designs
- Database of generalised quadrangles with spread
- Group-divisible designs (GDD)
- Incidence structures (i.e. hypergraphs, i.e. set systems)
- Mutually orthogonal Latin squares (MOLS)
- Bounds on the number of mutually orthogonal Latin squares
- Orthogonal arrays (OA)
- Orthogonal arrays (build recursive constructions)
- Orthogonal arrays (find recursive constructions)
- Resolvable balanced incomplete block design (RBIBD)
- Steiner quadruple systems
- Hypergraph isomorphic copy search
- Two-graphs
- Combinatorial diagrams
- Diagram and partition algebras
- Exact cover problem via dancing links
- Dyck words
- Enumerated sets
- Tools for enumeration modulo the action of a permutation group
- Substitutions over unit cube faces (Rauzy fractals)
- Bell and Uppuluri-Carpenter numbers
- Families
- Brent Yorgey’s fast algorithm for integer vector (multiset) partitions
- Finite state machines, automata, transducers
- Common automata and transducers (finite state machines generators)
- Free quasi-symmetric functions
- Free dendriform algebras
- Free modules
- Free pre-Lie algebras
- Fully commutative elements of Coxeter groups
- Fully packed loops
- Gelfand-Tsetlin patterns
- Paths in directed acyclic graphs
- Gray codes
- Grossman-Larson Hopf algebras
- Growth diagrams and dual graded graphs
- Hall polynomials
- The Hillman-Grassl correspondence
- Enumerated set of lists of integers with constraints: base classes
- Enumerated set of lists of integers with constraints, in inverse lexicographic order
- Enumerated set of lists of integers with constraints: front-end
- Lists of nonnegative integers with constraints.
- Counting, generating, and manipulating nonnegative integer matrices
- Nonnegative integer vectors
- Integer vectors modulo the action of a permutation group
- Weighted integer vectors
- Tamari Interval-posets
- Kazhdan-Lusztig polynomials
- Key polynomials
- Knutson-Tao puzzles
- Strong and weak tableaux
- Littlewood-Richardson tableaux
- Combinatorics on matrices
- Dancing Links internal pyx code
- Dancing links C++ wrapper
- Hadamard matrices
- Latin squares
- Miscellaneous
- Ordered multiset partitions into sets and the minimaj crystal
- Noncommutative symmetric functions and quasi-symmetric functions
- Common combinatorial tools
- Generic code for bases
- Noncommutative symmetric functions
- Quasisymmetric functions
- Introduction to quasisymmetric functions
- Symmetric functions in non-commuting variables
- Bases for
NCSym
- Dual symmetric functions in non-commuting variables
- Symmetric functions in noncommuting variables
- Necklaces
- Non-decreasing parking functions
- \(\nu\)-Dyck words
- \(\nu\)-Tamari lattice
- Ordered rooted trees
- Output functions
- Parallelogram polyominoes
- Parking functions
- Integer partitions
- Partition/diagram algebras
- Kleshchev partitions
- Iterators over the partitions of an integer
- Partition shifting algebras
- Partition tuples
- Path tableaux
- Catalog of path tableaux
- Dyck paths
- Frieze patterns
- Path tableaux
- Semistandard tableaux
- Perfect matchings
- Permutations
- Permutations (Cython file)
- Plane partitions
- Posets
- Bubble and Shuffle lattices
- Cartesian products of posets
- D-complete posets
- Elements of posets, lattices, semilattices, etc.
- Forest posets
- Some fast computations for finite posets
- Some fast computations for finite posets using FLINT matrices
- Hasse diagrams of posets
- Hochschild lattices
- Incidence algebras
- Finite lattices and semilattices
- Fast linear extension iterator
- Linear extensions of posets
- Mobile posets
- Möbius algebras
- Catalog of posets and lattices
- Finite posets
- \(q\)-analogues
- \(q\)-Bernoulli numbers and polynomials
- Combinatorics quickref
- Rankers
- Recognizable series
- \(k\)-regular sequences
- Boundedness of \(k\)-Regular Sequences
- Restricted growth arrays
- Ribbons
- Ribbon shaped tableaux
- Ribbon tableaux
- Rigged configurations
- Abstract classes for the rigged configuration bijections
- Bijection between rigged configurations and KR tableaux
- Bijection between rigged configurations for \(B(\infty)\) and marginally large tableaux
- Bijection classes for type \(A_n^{(1)}\)
- Bijection classes for type \(A_{2n}^{(2)\dagger}\)
- Bijection classes for type \(A_{2n}^{(2)}\)
- Bijection classes for type \(A_{2n-1}^{(2)}\)
- Bijection classes for type \(B_n^{(1)}\)
- Bijection classes for type \(C_n^{(1)}\)
- Bijection classes for type \(D_n^{(1)}\)
- Bijection classes for type \(D_4^{(3)}\)
- Bijection classes for type \(D_{n+1}^{(2)}\)
- Bijection classes for type \(E_{6,7}^{(1)}\)
- Kleber trees
- Kirillov-Reshetikhin tableaux
- Crystal of rigged configurations
- Rigged configurations of \(\mathcal{B}(\infty)\)
- Rigged configuration elements
- Rigged configurations
- Rigged partitions
- Tensor product of Kirillov-Reshetikhin tableaux
- Tensor product of Kirillov-Reshetikhin tableaux elements
- Rooted (unordered) trees
- Root systems
- Ambient lattices and ambient spaces
- Associahedron
- Braid move calculator
- Braid orbit
- Branching rules
- Cartan matrices
- Cartan types
- Coxeter groups
- Coxeter matrices
- Coxeter types
- Dynkin diagrams
- Extended affine Weyl groups
- Fundamental group of an extended affine Weyl group
- Hecke algebra representations
- Integrable representations of affine Lie algebras
- Nonsymmetric Macdonald polynomials
- Pieri factors
- Tutorial: visualizing root systems
- Reflection groups: auxiliary Cython functions
- Finite complex reflection groups
- Reflection group elements
- Finite real reflection groups
- Group algebras of root lattice realizations
- Root lattice realizations
- Root lattices and root spaces
- Root systems
- Root system data for type A
- Root system data for (untwisted) type A affine
- Root system data for affine Cartan types
- Root system data for type A infinity
- Root system data for type B
- Root system data for (untwisted) type B affine
- Root system data for type BC affine
- Root system data for type C
- Root system data for (untwisted) type C affine
- Root system data for type D
- Root system data for (untwisted) type D affine
- Root system data for dual Cartan types
- Root system data for type E
- Root system data for (untwisted) type E affine
- Root system data for type F
- Root system data for (untwisted) type F affine
- Root system data for folded Cartan types
- Root system data for type G
- Root system data for (untwisted) type G affine
- Root system data for type H
- Root system data for type I
- Root system data for Cartan types with marked nodes
- Root system data for type Q
- Root system data for reducible Cartan types
- Root system data for relabelled Cartan types
- Root system data for super type A
- Weight lattice realizations
- Weight lattices and weight spaces
- Weyl character rings
- Weyl groups
- Robinson-Schensted-Knuth correspondence
- Schubert polynomials
- Set partitions
- Fast set partition iterators
- Ordered set partitions
- Abreu-Nigro symmetric functions
- Symmetric functions
- Characters of the symmetric group as bases of the symmetric functions
- Classical symmetric functions
- Generic dual bases symmetric functions
- Elementary symmetric functions
- Hall-Littlewood polynomials
- Hecke character basis
- Homogeneous symmetric functions
- Jack symmetric functions
- Quotient of symmetric function space by ideal generated by Hall-Littlewood symmetric functions
- Kostka-Foulkes polynomials
- LLT symmetric functions
- Macdonald polynomials
- Monomial symmetric functions
- Multiplicative symmetric functions
- \(k\)-Schur functions
- Non-symmetric Macdonald polynomials
- Orthogonal symmetric functions
- Symmetric functions defined by orthogonality and triangularity
- Power sum symmetric functions
- Schur symmetric functions
- Symmetric functions, with their multiple realizations
- Symmetric functions
- Symplectic symmetric functions
- Witt symmetric functions
- Shard intersection order
- Shifted primed tableaux
- Shuffle product of iterables
- Sidon sets and their generalizations, Sidon \(g\)-sets
- Similarity class types of matrices with entries in a finite field
- sine-Gordon Y-system plotter
- Six vertex model
- Steinhaus-Johnson-Trotter algorithm
- Skew partitions
- Skew tableaux
- Functions that compute some of the sequences in Sloane’s tables
- Specht modules
- Combinatorial species
- Characteristic species
- Composition species
- Cycle species
- Empty species
- Functorial composition species
- Generating series
- Examples of combinatorial species
- Linear-order species
- Miscellaneous functions
- Partition species
- Permutation species
- Product species
- Recursive species
- Set species
- Combinatorial species
- Species structures
- Subset species
- Sum species
- Subsets
- Subsets satisfying a hereditary property
- Subsets whose elements satisfy a predicate pairwise
- Subwords
- Subword complex
- Subword complex: auxiliary Cython functions
- Super partitions
- Super tableaux
- Symmetric group algebra
- Representations of the symmetric group
- Tableaux
- Residue sequences of tableaux
- TableauTuples
- Generalized Tamari lattices
- Tiling solver
- Transitive ideal closure tool
- Combinatorial triangles for posets and fans
- T-sequences
- Tuples
- Combinatorics in Sage
- Vector partitions
- Abstract word (finite or infinite)
- Combinatorics on words
- Alphabet
- Finite word
- Infinite word
- Lyndon words
- Morphic words
- Word morphisms/substitutions
- Word paths
- Shuffle product of words
- Suffix tries and suffix trees
- Word classes
- Fast word datatype using an array of unsigned char
- Datatypes for finite words
- Common words
- Datatypes for words defined by iterators and callables
- User-customizable options for words
- Set of words
- Yang-Baxter Graphs
- C-finite sequences